Abstract Two polysaccharides have been studied which approximate in structure to alternating copolymers, (−A−B) n , in which B is a residue of β- d -galactose-4sulphate and A is a residue of 3,6-anhydro-α- d -galactose (κ-carrageenan) or its 2-sulphate (ι-carrageenan). The glycoside linkages are Al→3B and B1→4A. A small proportion of A residues also occur as α- d -galactose-6-sulphate and 2,6-disulphate in the natural polymers but were removed by fractionation or conversion to the anhydride with alkaline borohydride. X-ray diffraction photographs of oriented fibres of salts with various monovalent cations then showed fibre axis repeat distances of 24.6 A (κ-carrageenan) and 13.0 A (ι-carrageenan). Very similar models can be proposed for both polysaccharides, based on striking relationships between features in the various diffraction photographs, mathematical derivation of all models with appropriate dimensions and symmetry, and calculation of cylindrically averaged Fourier transforms. They are double helices with three disaccharide residues in a complete turn of each single chain, in 24.6 A (κ-carrageenan) or 26.0 A (ι-carrageenan). In ι-carrageenan the second chain is displaced exactly half a pitch from the first.